Probability
Probability
nta_pyq_2025_jan
Grade 12
Question:
Bag $B_{1}$ contains $6$ white and $4$ blue balls, Bag $B_{2}$ contains $4$ white and $6$ blue balls, and Bag $B_{3}$ contains $5$ white and $5$ blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability that the ball is drawn from Bag $B_{2}$ is:
$\dfrac{4}{15}$
$\dfrac{1}{3}$
$\dfrac{2}{5}$
$\dfrac{2}{3}$
Step-by-Step Solution
Key Concept: Bayes' theorem: $P(B_{2}|W)=\dfrac{P(B_{2})P(W|B_{2})}{\sum_{i}P(B_{i})P(W|B_{i})}.$
$P(B_{i})=\dfrac{1}{3}$ each. $P(W|B_{1})=\dfrac{6}{10},\,P(W|B_{2})=\dfrac{4}{10},\,P(W|B_{3})=\dfrac{5}{10}.$
$P(W)=\dfrac{1}{3}\!\left(\dfrac{6+4+5}{10}\right)=\dfrac{15}{30}=\dfrac{1}{2}.$
$P(B_{2}|W)=\dfrac{(1/3)(4/10)}{1/2}=\dfrac{4/30}{1/2}=\dfrac{4}{15}.$
Correct Answer: 1